3x(x-4)+x=-2

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Solution for 3x(x-4)+x=-2 equation:


Simplifying
3x(x + -4) + x = -2

Reorder the terms:
3x(-4 + x) + x = -2
(-4 * 3x + x * 3x) + x = -2
(-12x + 3x2) + x = -2

Reorder the terms:
-12x + x + 3x2 = -2

Combine like terms: -12x + x = -11x
-11x + 3x2 = -2

Solving
-11x + 3x2 = -2

Solving for variable 'x'.

Reorder the terms:
2 + -11x + 3x2 = -2 + 2

Combine like terms: -2 + 2 = 0
2 + -11x + 3x2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
0.6666666667 + -3.666666667x + x2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + -3.666666667x + -0.6666666667 + x2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + -3.666666667x + x2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + -3.666666667x + x2 = 0 + -0.6666666667
-3.666666667x + x2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
-3.666666667x + x2 = -0.6666666667

The x term is -3.666666667x.  Take half its coefficient (-1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
-3.666666667x + 3.361111114 + x2 = -0.6666666667 + 3.361111114

Reorder the terms:
3.361111114 + -3.666666667x + x2 = -0.6666666667 + 3.361111114

Combine like terms: -0.6666666667 + 3.361111114 = 2.6944444473
3.361111114 + -3.666666667x + x2 = 2.6944444473

Factor a perfect square on the left side:
(x + -1.833333334)(x + -1.833333334) = 2.6944444473

Calculate the square root of the right side: 1.641476301

Break this problem into two subproblems by setting 
(x + -1.833333334) equal to 1.641476301 and -1.641476301.

Subproblem 1

x + -1.833333334 = 1.641476301 Simplifying x + -1.833333334 = 1.641476301 Reorder the terms: -1.833333334 + x = 1.641476301 Solving -1.833333334 + x = 1.641476301 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x = 1.641476301 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = 1.641476301 + 1.833333334 x = 1.641476301 + 1.833333334 Combine like terms: 1.641476301 + 1.833333334 = 3.474809635 x = 3.474809635 Simplifying x = 3.474809635

Subproblem 2

x + -1.833333334 = -1.641476301 Simplifying x + -1.833333334 = -1.641476301 Reorder the terms: -1.833333334 + x = -1.641476301 Solving -1.833333334 + x = -1.641476301 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x = -1.641476301 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = -1.641476301 + 1.833333334 x = -1.641476301 + 1.833333334 Combine like terms: -1.641476301 + 1.833333334 = 0.191857033 x = 0.191857033 Simplifying x = 0.191857033

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.474809635, 0.191857033}

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